∫ 3/(25·x^2 - 20·x + 7) dx
= 3/25 ∫ 1/(x^2 - 4/5·x + 7/25) dx
= 3/25 ∫ 1/(x^2 - 4/5·x + 4/25 + 3/25) dx
= 3/25 ∫ 1/((x - 2/5)^2 + 3/25) dx
Subst. t = x - 2/5
= 3/25 ∫ 1/(t^2 + 3/25) dt
= 3/25 · 1/√(3/25) · arctan(1/√(3/25)·t) + C
Resubst.
= 3/25 · 1/√(3/25) · arctan(5/√3·(x - 2/5)) + C
= √3/5 · arctan((5·x - 2)/√3) + C